A Semiclassical, Entropic Proof of a Weak Gravity Conjecture

Abstract

We present a semiclassical proof of the weak gravity conjecture in $D=4$ spacetime dimensions for scalar matter gauged under a $U(1{)}^N$ gauge group. We compute the non-perturbative macroscopic entropy of a scalar field in an extremal black hole background at the level of linearized backreaction on the metric. The scalar field is assumed to violate or saturate the weak gravity conjecture. The scalar contributes a logarithmic correction to the entropy in the black hole geometry that outgrows the classical contribution. We demonstrate that the entropy of the gauged scalar violates the generalized second law in the limit of large black hole charge. Our result suggests that entropy inequalities may directly discriminate between effective field theories that live in the landscape versus the swampland.

arXiv commentv3: 25 pages, clarified main result of the paper and created section on consistency checks on main argument;v2: 25 pages, significantly expanded discussion on renormalization and backreaction to demonstrate validity of our results

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• On the weak gravity conjecture in string theory with broken supersymmetry
• A universal formula for the density of states in theories with finite-group symmetry
• Towards a proof of the Weak Gravity Conjecture
• Weak Gravity Conjecture From Low Energy Observers' Perspective